1. Technical Field
The present invention relates to a Lamb-wave resonator and an oscillator equipped with the Lamb wave resonator.
2. Related Art
A Lamb wave is a plate wave, which is a bulk wave propagates inside a substrate while being repeatedly reflected by upper and lower surfaces of the substrate in the case in which the substrate is arranged to have a thickness equal to or smaller than several wavelengths of the wave to be propagated. In contrast to a surface wave having 90% of the energy thereof in areas with a depth of within one wavelength from the surfaces of the substrate, such as a Rayleigh wave, a leaky surface acoustic wave, or a quasi longitudinal leaky surface acoustic wave, the Lamb wave is a bulk wave propagating inside the substrate, and therefore, the energy thereof is distributed throughout the entire substrate.
According to “Ultrasonic Wave Handbook” edited by Ultrasonic Wave Handbook Editorial Committee, published by Maruzen Co., Ltd. in 1999, pp. 62-71, plate waves and Rayleigh waves are also distinguished academically. Further, in “Acoustic Wave Element Technical Handbook” edited by the 150th committee of the Nippon Academy Promotion Association, published by Ohmsha, Ltd. in 1991, pp. 148-158, there is disclosed a method for analyzing Rayleigh waves and leaky surface acoustic waves, and in “Temperature characteristics of the substrate for lamb wave type elastic wave devices” by Yasuhiko Nakagawa, Mitsuyoshi Shigeda, Kazumasa Shibata, and Shouji Kakio, IEICE Transactions on Electronics J-89C No. 1, pp. 34-39, there is disclosed a method for analyzing Lamb waves. As a big difference therebetween, there can be cited a difference in method of selecting the solution of the eighth equation between the waves, and therefore, Rayleigh waves and Lamb waves are completely different waves having properties different from each other. Therefore, since Lamb waves cannot provide favorable characteristics under design conditions the same as those of Rayleigh waves, a design approach specified for Lamb waves is required.
As a feature of Lamb waves, as shown in the dispersion curve disclosed in JP-A-2003-258596, a mode of Lamb waves, which can be propagated, is a mode in which a wave number in a thickness direction of a substrate satisfies resonance conditions, and Lamb waves have a number of modes including high order ones.
Since the phase velocity of the existing modes of Lamb waves is equal to or higher than that of Rayleigh waves, and many of the modes have a phase velocity equal to or higher than that of longitudinal waves, the higher the phase velocity of the mode is, the more easily the higher frequency can be achieved even in the case in which the width of the electrode fingers is the same as that in the case of the surface wave described above. Further, by using an AT cut quartz substrate having a thickness of 5 wavelengths or less, it becomes possible to use Lamb waves having an excellent temperature characteristic and suitable for achieving a high frequency.
According to JP-A-2003-258596 described above, there is described that metal having a higher specific gravity is used as an electrode, thereby making it possible to increase a reflection coefficient of Lamb waves, and to trap the energy with less number of reflectors, and therefore, downsizing becomes possible. This means that energy trapping is achieved by suppressing a vibration leakage in a lengthwise direction (a propagation direction of Lamb waves). However, it is hard to say that this electrode design is always optimum because energy trapping in a widthwise direction (a direction perpendicular to the propagation direction of Lamb waves) is not considered. Further, JP-A-2008-54163 also fails to disclose specific measures to enhance energy trapping in the widthwise direction.
If the vibration leakage occurs in the widthwise direction (a direction perpendicular to the propagation direction of the Lamb wave), it is possible that it is difficult to take full advantage of the preferable characteristic of the Lamb waves, and degradation of the Q-value and increase in the CI-value, both the important factors in evaluating the resonance characteristic, are incurred. As a result, a sufficient characteristic is not obtained when applying it to an oscillator, and increase in power consumption and a serious problem of stoppage of oscillation are caused.
Further, if the vibration leakage in the widthwise direction reaches the widthwise outer end of the piezoelectric substrate, a spurious is caused by a reflected wave from the outer end of the piezoelectric substrate.